Man-made composite material and man-made composite material antenna
View Patent ↗The present invention relates to a man-made composite material. The man-made composite material is divided into a plurality of regions. A plane electromagnetic wave is incident on a first surface and exits in the form of a spherical wave from a second surface of the man-made composite material opposite to the first surface. Reverse extensions of the exiting electromagnetic wave intersect with each other at a virtual focus of the man-made composite material. A line connecting the virtual focus to a point on the top surface of the i th region and a line perpendicular to the man-made composite material form an angle θ therebetween, which uniquely corresponds to a curved surface in the i th region. A set formed by points on the top surface of the i th region that have the same angle θ forms a boundary of the curved surface to which the angle θ uniquely corresponds.
1. A man-made composite material having a thickness between a first and second surface, configured such that the first and second surfaces are perpendicularly disposed to a propagation direction of a plane electromagnetic wave, wherein the man-made composite material is divided into a plurality of regions; the plane electromagnetic wave is incident on the first surface of the man-made composite material and a spherical electromagnetic wave exits from the second surface of the man-made composite material opposite to the first surface;
reverse extensions of the exiting spherical electromagnetic wave intersect with each other at a virtual focus of the man-made composite material; an i th region is one of the plurality of regions, where i is a positive integer and selected from a group consisting of 1, 2, 3, . . . , etc.;
an intersection between the i th region and the first surface is a bottom surface of the i th region, an intersection between the i th region and the second surface is a top surface of the i th region, and each i th region has a curved surface extending from the top surface to the bottom surface;
each i th region having a set of first straight lines connecting the virtual focus to a corresponding set of points on a circular boundary line between the i th region's curved surface and the i th region's top surface, and a second straight line perpendicular to the man-made composite material, wherein each first straight line forms an angle θ with the second straight line, wherein the same angle θ corresponds to each of the points in the set of points;
each i th region having additional sets of first straight lines connecting the virtual focus to additional corresponding sets of points along the i th region's curved surface, wherein each additional set of points on the i th region's curved surface form a circular line and has a same uniquely corresponding angle θ and a same refractive index; each i th region's curved surface has a generatrix which extends between the bottom surface and the top surface of the i th region and is formed by rotating the generatrix about the second straight line; and refractive indices of each of the regions increase gradually as the angle θ increases.
2. The man-made composite material of claim 1 , wherein a line connecting the virtual focus to a point on an outer circumference of the top surface of the i th region and the line perpendicular to the man-made composite material form an angle θ i therebetween, i is a positive integer, and the closer the region is to a center of the man-made composite material, the smaller the value of i will be; wherein a generatrix of a curved surface to which the angle θ i corresponds has an arc length c(θ i ) and the arc length c(θ i ) and the angle θ i satisfy the following equations:
c
(
θ
i
)
=
λ
n
max
(
i
)
-
n
min
(
i
+
1
)
;
(
s
+
d
)
×
(
1
cos
θ
i
-
1
cos
θ
i
-
1
)
=
c
(
θ
i
)
n
max
(
i
)
-
c
(
θ
i
-
1
)
n
min
(
i
)
)
,
where, θ 0 =0, c(θ 0 )=d ; s is a distance from the virtual focus to the man-made composite material; d is a thickness of the man-made composite material; λ is a wavelength of an electromagnetic wave, n max(i) and n min(i) are the maximum refractive index and the minimum refractive index of the i th region respectively, and n max(i+1) is the maximum refractive index of the (i+1) th region.
3. The man-made composite material of claim 2 , wherein the maximum refractive indices and the minimum refractive indices of any two adjacent ones of the regions satisfy: n max(i) −n min(i) =n max(i+1) −n min(i+1) .
4. The man-made composite material of claim 3 , wherein the maximum refractive indices and the minimum refractive indices of any three adjacent ones of the regions satisfy: n max(i+1) −n min(i+2) >n max(i) −n min(i+1) .
5. The man-made composite material of claim 2 , wherein a refractive index distribution of the i th region satisfies:
n
i
(
θ
)
=
1
c
(
θ
)
[
(
s
+
d
)
cos
θ
-
(
s
+
d
)
+
n
min
d
]
where c(θ) is an arc length of a generatrix of the curved surface to which the angle θ corresponds, s is the distance from the virtual focus to the man-made composite material, d is the thickness of the man-made composite material, and n min is the minimum refractive index of the man-made composite material.
6. The man-made composite material of claim 1 , wherein the generatrix of the curved surface is a parabolic arc.
7. The man-made composite material of claim 6 , wherein when a line passing through a center of the second surface of the man-made composite material and perpendicular to the man-made composite material is taken as an abscissa axis and a line passing through the center of the second surface of the man-made composite material and parallel to the second surface is taken as an ordinate axis, an equation of a parabola where the parabolic arc is located is represented as:
y ( x ) =ax 2 +bx+c
where a, b and c satisfy the following relationships:
c =( s+d )tan θ;
2 ad+b= 0.
8. The man-made composite material of claim 7 , wherein the arc length c(θ) of the parabolic arc satisfies the following equation:
c
(
θ
)
=
d
2
[
log
(
tan
θ
+
1
+
tan
2
θ
)
+
δ
tan
θ
+
δ
+
1
+
tan
2
θ
]
where δ is a preset decimal.
9. The man-made composite material of claim 1 , wherein the generatrix of the curved surface is an elliptical arc.
10. The man-made composite material of claim 9 , wherein when the line passing through the center of the second surface of the man-made composite material and perpendicular to the man-made composite material is taken as an abscissa axis and the line passing through the center of the second surface of the man-made composite material and parallel to the second surface is taken as an ordinate axis, an equation of an ellipse where the elliptical arc is located is represented as:
(
x
-
d
)
2
a
2
+
(
y
-
c
)
2
b
2
=
1
where a, b and c satisfy the following relationships:
d
2
a
2
+
[
(
s
+
d
)
tan
θ
-
c
]
2
b
2
=
1
;
sin
θ
n
2
(
θ
)
-
sin
2
(
θ
)
=
b
2
a
2
d
(
s
+
d
)
tan
θ
-
c
.
11. A man-made composite material antenna, comprising a radiation source and a man-made composite material, the man-made composite material having a thickness between a first and second surface, configured such that the first and second surfaces are perpendicularly disposed to a propagation direction of a plane electromagnetic wave, wherein the man-made composite material is divided into a plurality of regions; the plane electromagnetic wave is incident on the first surface of the man-made composite material and a spherical electromagnetic wave exits from the second surface of the man-made composite material opposite to the first surface; reverse extensions of the exiting spherical electromagnetic wave intersect with each other at a virtual focus of the man-made composite material; an i th region is one of the plurality of regions, where i is a positive integer and selected from a group consisting of 1, 2, 3, . . . , etc.;
an intersection between a the i th region and the first surface is a bottom surface of the i th region, an intersection between the i th region and the second surface is a top surface of the i th region, and each i th region has a curved surface extending from the top surface to the bottom surface;
each i th region having a set of first straight lines connecting the virtual focus to a corresponding set of points on a circular boundary line between the i th region's curved surface and the i th region's top surface, and a second straight line perpendicular to the man-made composite material, wherein each first straight line forms an angle θ with the second straight line, wherein the same angle θ corresponds to each of the points in the set of points;
each i th region having additional sets of first straight lines connecting the virtual focus to additional corresponding sets of points along the i th region's curved surface, wherein each additional set of points on the i th region's curved surface form a circular line and has a same uniquely corresponding angle θ and a same refractive index; each i th region's curved surface has a generatrix which extends between the bottom surface and the top surface of the i th region and is formed by rotating the generatrix about the second straight line; and refractive indices of each of the regions increase gradually as the angle θ increases.
12. The man-made composite material antenna of claim 11 , wherein a line connecting the virtual focus to a point on an outer circumference of the top surface of the i th region and the line perpendicular to the man-made composite material form an angle θ i therebetween, i is a positive integer, and the closer the region is to a center of the man-made composite material, the smaller the value of i will be; wherein a generatrix of a curved surface to which the angle θ i corresponds has an arc length c(θ i ) , and the arc length c(θ i ) and the angle θ i satisfy the following equations:
c
(
θ
i
)
=
λ
n
max
(
i
)
-
n
min
(
i
+
1
)
;
(
s
+
d
)
×
(
1
cos
θ
i
-
1
cos
θ
i
-
1
)
=
c
(
θ
i
)
n
max
(
i
)
-
c
(
θ
i
-
1
)
n
min
(
i
)
)
,
where, θ 0 =0, c(θ 0 )=d; s is a distance from the virtual focus to the man-made composite material; d is a thickness of the man-made composite material; λ is a wavelength of an electromagnetic wave, n max(i) and n min(i) are maximum refractive index and the minimum refractive index of the i th region respectively, and n max(i+1) is the maximum refractive index of the (i+1) th region.
13. The man-made composite material antenna of claim 12 , wherein the maximum refractive indices and the minimum refractive indices of any two adjacent ones of the regions satisfy:
n max(i) −n min(i) =n max(i+1) −n min(i+1) .
14. The man-made composite material antenna of claim 13 , wherein the maximum refractive indices and the minimum refractive indices of any three adjacent ones of the regions satisfy:
n max(i+1) −n min(i+2) >n max(i) −n min(i+1) .
15. The man-made composite material antenna of claim 12 , wherein a refractive index distribution of the i th region satisfies:
n
i
(
θ
)
=
1
c
(
θ
)
[
(
s
+
d
)
cos
θ
-
(
s
+
d
)
+
n
min
d
]
where c(θ) is an arc length of a generatrix of the curved surface to which the angle θ corresponds, s is the distance from the virtual focus to the man-made composite material, d is the thickness of the man-made composite material, and n min is the minimum refractive index of the man-made composite material.
16. The man-made composite material antenna of claim 11 , wherein the generatrix of the curved surface is a parabolic arc.
17. The man-made composite material antenna of claim 16 , wherein when a line passing through a center of the second surface of the man-made composite material and perpendicular to the man-made composite material is taken as an abscissa axis and a line passing through the center of the second surface of the man-made composite material and parallel to the second surface is taken as an ordinate axis, an equation of a parabola where the parabolic arc is located is represented as:
y ( x )= ax 2 +bx+c
where a, b and c satisfy the following relationships:
c =( s+d )tan θ;
2 ad+b= 0.
18. The man-made composite material antenna of claim 17 , wherein the arc length c(θ) of the parabolic arc satisfies the following equation:
c
(
θ
)
=
d
2
[
log
(
tan
θ
+
1
+
tan
2
θ
)
+
δ
tan
θ
+
δ
+
1
+
tan
2
θ
]
where δ is a preset decimal.
19. The man-made composite material antenna of claim 11 , wherein the generatrix of the curved surface is an elliptical arc.
20. The man-made composite material antenna of claim 19 , wherein when the line passing through the center of the second surface of the man-made composite material and perpendicular to the man-made composite material is taken as an abscissa axis and the line passing through the center of the second surface of the man-made composite material and parallel to the second surface is taken as an ordinate axis, an equation of an ellipse where the elliptical arc is located is represented as:
(
x
-
d
)
2
a
2
+
(
y
-
c
)
2
b
2
=
1
where a, b and c satisfy the following relationships:
d
2
a
2
+
[
(
s
+
d
)
tan
θ
-
c
]
2
b
2
=
1
;
sin
θ
n
2
(
θ
)
-
sin
2
(
θ
)
=
b
2
a
2
d
(
s
+
d
)
tan
θ
-
c
.